Analysis on the empirical invasion networks

Introduction

• The R scripts (sourced in this Rmd) can be run externally to Rstudio.
• The R scripts are only for saving R functions, processing raw and temporary data.
• All visualization codes are in this Rmd file.

03A-make_network

• Make community network from data/output/pairs.csv.

• Plot networks and matrices

Make network

Pairwise matrice

Plot the communities’ pairwise matrix, whose axis are ordered by competitive ranks

Randomize networks

For record, it took 2603 seconds ~= 40 mins to generate 10000 randomized networks for all 13 communities.

It took ~50 seconds to randomize 1000 times for each of the communities. So total of 641 seconds needed.

The randomized networks are saved in data/output/network_randomized.Rdata which contains a two-layer R list net_randomized_list in which the first layer has the 13 communities and the second layer has 1000 randomized networks.

Example of randomized network matrix

03B-network_motifs

Detect motifs in networks

• networks_motif: data.frame
• networks_motif_randomized: data.frame for all randomized networks motif counts

Empirical network motifs. 13 communities x 7 motifs = 91 rows

Shuffled network motifs. 13 communities x 7 motifs x 1000 bootstraps = 91000 rows

Motif distributions

Detect motifs in randomized networks

Plot the histogram of randomized network motifs

03C-diagonal_analysis

Competitive hierarchy (unfinished)

The competitive scores for all pairs are converted into a pairwise competitive matrix, with a value of “1” representing a win and a value of “0” representing a loss. Pairings that resulted on a draw were assingned a value of 0.5, representing coexistence.

The competitive intransitivity is determined as follow

\[\frac{\sum I{a_{ij}<a_{ji}}}{n(n-1)/2}\]

Diagonal analysis

For record, it took 1655 seconds ~= 26 minutes to compute the diagonal measures for 13 communities X 10000 randomization, merge them into one single data frame.

data/output/networks_diag

data/output/networks_diag_randomized

For a network matrix \(m_{ij}\), the fraction of coexistence as a fucntion of distance to diagonal is calculated as the

\[\frac{}{\lvert i-j \lvert}\]

networks_diag_randomized has four columns

Randomization: the number of randomization

Plot the diagonal analysis

Summary

• isolates: 68 isolates
• pairs: 186 pairs
• communities: metadata of 13 communities
• network_community.Rdata saves one R lists. net_list has 13 tbl_graph objects. that describes the competitive networks of my communities, where p_net_list has 13 pictures.

isolates <- read_csv(here::here("data/output/isolates.csv"))

Rows: 100 Columns: 62
── Column specification ────────────────────────────────────────────────────────────────────
Delimiter: ","
chr  (8): Assembly, ExpID, Community, Family, Genus, Sequence, PreferredCS, SecretedCS
dbl (52): ID, Isolate, GenusScore, ColonyCount, DilutionFactor, Epsilon, Win, Lose, Draw...
lgl  (2): Fermenter, GramPositive

ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

pairs <- read_csv(here::here("data/output/pairs.csv"))

Rows: 248 Columns: 29
── Column specification ────────────────────────────────────────────────────────────────────
Delimiter: ","
chr (14): Assembly, Community, InteractionType, InteractionTypeFiner, ExpID1, Family1, G...
dbl (10): Isolate1, Isolate2, From, To, ID1, GenusScore1, ID2, GenusScore2, SeqDifferenc...
lgl  (5): Fermenter1, GramPositive1, Fermenter2, GramPositive2, Isolate1Dominant

ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

communities <- read_csv(here::here("data/output/communities.csv"))

Rows: 17 Columns: 4
── Column specification ────────────────────────────────────────────────────────────────────
Delimiter: ","
chr (1): Community
dbl (3): CommunitySize, CommunityPairSize, CommunitiyMotifSize

ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

load(here::here("data/output/network_community.Rdata"))

Convert the graph file into txt

So that the graph is readable in python

Error: object 'f' not found

Plot network in matrix

Upper half matrices

Plot network in graph

There are some functions to play with

Combine matrix and network plot

$C1R2
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$C11R5
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